For English speakers, I know of three heavyweights in the ``Kanji
Dictionary'' arena:

``Nelson'' -
The Modern Reader's Japanese-English
Character Dictionary
by Andrew Nelson, Tuttle, 1962.
The old edition
is still available, but there's also a new edition
out, but I have not seen it.

``S&H'' -
The Kanji Dictionary
by Mark Spahn and Wolfgang Hadamitzky.
First published in 1989 by Nichigai Associates under the name
``Japanese Character Dictionary -
With Compound Lookup via Any Kanji,''
revised and republished in 1996 by Tuttle.

When considering these and others -- which to buy, which are good, which to
keep nearby on the shelf, etc. -- there are two primary concerns to keep in
mind:

What indexing method or methods are used to find the entry for a
particular character.

What information is available once you get there.

I'll address the second point first.

Information a ``Kanji Dictionary'' Provides

It is important to keep in mind that there are several completely
different types of reference works called ``Kanji Dictionaries.'' In
Japanese, this is usually written $B;zE5(J (jiten)
which happens to be pronounced the same as $B(J,
which is a more traditional ``dictionary.''

Works might have their PRIMARY GOAL to

provide meanings of words -
Provides translations of words from Japanese to English, but has them
ordered and grouped via kanji rather than pronunciation. Examples are
Nelson, S&H, edict, and the Canon Word Tank (which is also a normal
dictionary as well),

provide an understanding of how a kanji is used -
Provide information helpful for the student of Japanese kanji, for study.
This might well include words (as is the primary goal of the type above)
and data (primary goal of the type below), but this information is only
provided as support toward the overal goal of showing how the character is
used in Japanese. Important also are discussions of the ``feel'' a
character might give a word, examples of use with relevent grammatical
comments, notes on common mistakes and areas of confusion, and perhaps
stroke-order diagrams. An example is Halpern.

provide data about kanji -
Some might describes in detail information related to a kanji. Its
readings, perhaps its encodings via various human and computer encoding
standards. Perhaps variant forms, old forms, and forms from other
languages. Perhaps its etymology and stroke ordering as well. An example is
kanjidic and the JIS X 0208 standard.

I've never seen one work that encompasses everything.

If you merely want to look up words

For looking up words, S&H or Nelson are probably what you want. I have
never used Nelson, but it has been ``the standard'' since long before I was
born.

For the most part, these kinds of ``Kanji Dictionaries'' are really ``Word
Dictionaries'' with the entries arranged via kanji. In fact, the Japanese
title of S&H translates to ``Kanji-English Word Dictionary'', which is
really more appropriate than ``The Kanji Dictionary''.

Often, these works limit their attention to jukugo, words
composed of combinations of kanji, for the most part giving light or no
treatment to the kun'yomi meanings of a character. For example, the
character $B3](J is the ka in `kakeru',
`kake', `kakaru', and `kakari'. Yet the many meanings of these
stand-alone words are often glossed over or ignored. Contrast this with
Halpern below.

For the most part, English translation is simply a word or two -- this is
usually enough to give a good indication, but once the reading is known, a
``real'' dictionary should be checked if there are still questions. This
makes these works ``glossaries'', not ``dictionaries'', but few make the
distinction (heck, I call my server a ``dictionary server'' but it uses
edict, which is certainly a glossary).

If you want to study kanji

If you, as an English speaker, want to study kanji -- get a feel for their
practical use across the span of the language, then you want Halpern. The
purpose of Halpern is not to provide an exhaustive list of words, but
to provide a representative ``feel'' for how a character is used in
Japanese.

Halpern is not designed for bulk translation work; it is designed for
study. He presents detailed ``core meanings'' of each character, and
partitions a character's actual use in the language into senses that helps
the student absorb usage patterns. He gives equal attention to all types of
uses, including kun'yomi, on'yomi, independent, and
special readings. Examples are a mixture of not only isolated words, but
phrases and sentences with appropriate grammatical points of interest.
(See the dictionary's home page for a lot more information on
what it provides.)

To extend on the kakeru example from above,
consider what S&H says about this oft-used word: